### Transcription of Structural Equation Modeling Using AMOS

1 **Structural** **Equation** **Modeling** **Using** **amos** . An **introduction** August 2012. **Structural** **Equation** **Modeling** **Using** **amos** . Table of Contents Section 1: **introduction** ..3. About this Document/Prerequisites ..3. Accessing **amos** ..3. Documentation ..4. Getting Help with **amos** ..4. Section 2: SEM Basics ..5. Overview of **Structural** **Equation** **Modeling** ..5. SEM Why SEM? ..8. Section 3: SEM Assumptions ..8. A Reasonable Sample Size ..8. Continuously and Normally Distributed Endogenous Variables ..9. Model Identification (Identified **equations** ) ..9. Complete Data or Appropriate Handling of Incomplete Data .. 13. Theoretical Basis for Model Specification and 14. Section 4: Building and Testing a Model **Using** **amos** Graphics .. 15. Illustration of the SEM-Multiple Regression Relationship .. 15. Drawing a model **Using** **amos** Graphics .. 19. Reading Data into **amos** .. 26. Selecting **amos** Analysis Options and Running your Model .. 33. Section 5: Interpreting **amos** Output .. 35. Evaluating Global Model Fit.

2 36. Tests of Absolute Fit .. 38. Tests of Relative Fit .. 38. Modifying the Model to Obtain Superior Goodness of Fit .. 39. Viewing Path Diagram Output .. 46. Significance Tests of Individual Parameters .. 49. Section 6: Putting it all together - A substantive interpretation of the findings .. 50. References .. 51. 2. The Division of Statistics + Scientific Computation, The University of Texas at Austin **Structural** **Equation** **Modeling** **Using** **amos** . Section 1: **introduction** About this Document/Prerequisites This course is a brief **introduction** and overview of **Structural** **Equation** **Modeling** **Using** the **amos** (Analysis of Moment Structures) software. **Structural** **Equation** **Modeling** (SEM). encompasses such diverse statistical techniques as path analysis, confirmatory factor analysis, causal **Modeling** with latent variables, and even analysis of variance and multiple linear regression. The course features an **introduction** to the logic of SEM, the assumptions and required input for SEM analysis, and how to perform SEM analyses **Using** **amos** .

3 By the end of the course you should be able to fit **Structural** **Equation** models **Using** **amos** . You will also gain an appreciation for the types of research questions well-suited to SEM and an overview of the assumptions underlying SEM methods. You should already know how to conduct a multiple linear regression analysis **Using** SAS, SPSS, or a similar general statistical software package. You should also understand how to interpret the output from a multiple linear regression analysis. Finally, you should understand basic Microsoft Windows navigation operations: opening files and folders, saving your work, recalling previously saved work, etc. Accessing **amos** . You may access **amos** in one of three ways: 1. License a copy from SPSS, Inc. for your own personal computer. 2. **amos** is available to faculty, students, and staff at the University of Texas at Austin via the STATS Windows terminal server. To use the terminal server, you must obtain an ITS. computer account (an IF or departmental account) and then validate the account for Windows NT Services.

4 You then download and configure client software that enables your PC, Macintosh, or UNIX workstation to connect to the terminal server. Finally, you connect to the server and launch **amos** by double-clicking on the **amos** program icon located in the STATS terminal server program group. Details on how to obtain an ITS. computer account, account use charges, and downloading client software and configuration instructions may be found in 3. Download the free student version of **amos** from the **amos** development website for your own personal computer. If your models of interest are small, the free demonstration version may be sufficient to meet your needs. For larger models, you will need to purchase your own copy of **amos** or access the ITS shared copy of the software through the campus network. The latter option is typically more cost effective, particularly if you decide to access the other software programs available on the server ( , SAS, SPSS, HLM, Mplus, etc.)

5 3. The Division of Statistics + Scientific Computation, The University of Texas at Austin **Structural** **Equation** **Modeling** **Using** **amos** . Documentation The **amos** manual is the **amos** User's Guide by James Arbuckle and can be found online. It contains over twenty examples that map to models typically fitted by many investigators. These same examples, including sample data, are included with the student and commercial versions of **amos** , so you can easily fit and modify the models described in the **amos** manual. The previous **amos** manual is the **amos** User's Guide by James Arbuckle and Werner Wothke; this manual also contains numerous examples. A copy of the **amos** User's Guide is available at the PCL for check out by faculty, students, and staff at UT Austin. Barbara Byrne has also written a book on **Using** **amos** . The title is **Structural** **Equation** **Modeling** with **amos** : Basic Concepts, Applications, and Programming. The book is published by Lawrence Erlbaum Associates, Inc.

6 Lawrence Erlbaum Associates, Inc. also publishes the journal **Structural** **Equation** **Modeling** on a quarterly basis. The journal contains software reviews, empirical articles, and theoretical pieces, as well as a teacher's section and book reviews. A number of textbooks about SEM are available, ranging from Ken Bollen's encyclopedic reference book to Rick Hoyle's more applied edited volume. Several commonly cited titles are shown below. Bollen, (1989). **Structural** **equations** with Latent Variables. New York: John Wiley and Sons. Loehlin, (1997). Latent Variable Models. Mahwah, NJ: Lawrence Erlbaum Associates. Hoyle, R. (1995). **Structural** **Equation** **Modeling** : Concepts, Issues, and Applications. Thousand Oaks, CA: Sage Publications. Hatcher, L. (1996). A Step-by-Step Approach to **Using** the SAS System for Factor Analysis and **Structural** **Equation** **Modeling** . Cary, NC: SAS Institute, Inc. Getting Help with **amos** . If you have difficulties accessing **amos** on the STATS Windows terminal server, call the ITS.

7 Helpdesk at 512-475-9400 or send e-mail to If you are able to log in to the Windows NT terminal server and run **amos** , but have questions about how to use **amos** or interpret output, schedule an appointment with a statistical consultant at SSC statistical consulting or send e-mail to Important note: Both services are available to University of Texas faculty, students, and staff only. See our Web site at for more details about consulting services, as well as frequently asked questions and answers about EFA, CFA/SEM, **amos** , and other topics. 4. The Division of Statistics + Scientific Computation, The University of Texas at Austin **Structural** **Equation** **Modeling** **Using** **amos** . Non-UT and UT **amos** users will find Ed Rigdon's SEM FAQ Web site to be a useful resource; see the information on the SEMNET online discussion group for information on how to subscribe to this forum to post questions and learn more about SEM. Section 2: SEM Basics Overview of **Structural** **Equation** **Modeling** SEM is an extension of the general linear model (GLM) that enables a researcher to test a set of regression **equations** simultaneously.

8 SEM software can test traditional models, but it also permits examination of more complex relationships and models, such as confirmatory factor analysis and time series analyses. The basic approach to performing a SEM analysis is as follows: 5. The Division of Statistics + Scientific Computation, The University of Texas at Austin **Structural** **Equation** **Modeling** **Using** **amos** . The researcher first specifies a model based on theory, then determines how to measure constructs, collects data, and then inputs the data into the SEM software package. The package fits the data to the specified model and produces the results, which include overall model fit statistics and parameter estimates. The input to the analysis is usually a covariance matrix of measured variables such as survey item scores, though sometimes matrices of correlations or matrices of covariances and means are used. In practice, the data analyst usually supplies SEM programs with raw data, and the programs convert these data into covariances and means for its own use.

9 The model consists of a set of relationships among the measured variables. These relationships are then expressed as restrictions on the total set of possible relationships. The results feature overall indexes of model fit as well as parameter estimates, standard errors, and test statistics for each free parameter in the model. SEM Nomenclature SEM has a language all its own. Statistical methods in general have this property, but SEM users and creators seem to have elevated specialized language to a new level. Independent variables, which are assumed to be measured without error, are called exogenous or upstream variables; dependent or mediating variables are called endogenous or downstream variables. Manifest or observed variables are directly measured by researchers, while latent or unobserved variables are not directly measured but are inferred by the relationships or correlations among measured variables in the analysis. This statistical estimation is accomplished in much the same way that an exploratory factor analysis infers the presence of latent factors from shared variance among observed variables.

10 SEM users represent relationships among observed and unobserved variables **Using** path diagrams. Ovals or circles represent latent variables, while rectangles or squares represent measured variables. Residuals are always unobserved, so they are represented by ovals or circles. In the diagram shown below, correlations and covariances are represented by bidirectional arrows, which represent relationships without an explicitly defined causal direction. For instance, F1 and F2 are related or associated, but no claim is made about F1 causing F2, or vice versa. 6. The Division of Statistics + Scientific Computation, The University of Texas at Austin **Structural** **Equation** **Modeling** **Using** **amos** . By contrast, we do claim that F1 causes the scores observed on the measured variables I1 and I2. Causal effects are represented by single-headed arrows in the path diagram. F1 and F2 can be conceptualized as the variance the two indicators share ( , what the two indicators have in common.)